How do you convert 25 degrees, 15 minutes, and 30 seconds to decimal degrees?

To convert an angle given in degrees, minutes, and seconds to decimal degrees, you use the following procedure:

1. Start with the number of degrees, which remain unchanged in the conversion. In this case, you have 25 degrees.

2. Convert the minutes into decimal degrees. Since there are 60 minutes in a degree, you divide the number of minutes by 60. Here, you have 15 minutes: [ 15 , \text{minutes} \div 60 = 0.25 , \text{degrees} ]

3. Next, convert the seconds into decimal degrees. There are 3600 seconds in a degree (60 seconds in a minute multiplied by 60 minutes in a degree). You divide the number of seconds by 3600. In this case, you have 30 seconds: [ 30 , \text{seconds} \div 3600 = 0.0083333 , \text{degrees} ]

4. Now, add all these values together to get the total in decimal degrees: [ 25 + 0.25 + 0.0083333 = 25.258333